Which system of linear inequalities has the point 2 1

Posted By Admin @ November 26, 2022

Question:

Which system of linear inequalities has the point (2 ,1) in its solution set?

The system of Linear equation is x + 2y ≤ 4 and 2x - y > 0

Step-by-step explanation:

Given: Point ( 2 , 1 )

To find: System of Linear Inequalities which contain given point in

its solution set

There are 2 lines passing through point ( 2 , 1 )

So first we find the equation of both lines

Equation of line using Two-Point form is given by,

Equation of line 1 passing through ( 0 , 2 ) & ( 4 , 0 )

....... (1)

Equation line 2 passing through ( 0 , 0 )  & ( 2 , 1 )

....... (2)

Now from given graph is clear line 1 contain the given point and area shaded by it is toward origin then we have less than equal sign,

⇒ x + 2y ≤ 4

Line 2 is dotted line. So, it does not contain the given point and area shaded by it is toward 4th quadrant then we have greater than sign in it.

⇒ 2x - y > 0

Therefore, The system of Linear equation is x + 2y ≤ 4 and 2x - y > 0

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